Topological Autoencoders

Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:7045-7054, 2020.

Abstract

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-moor20a, title = {Topological Autoencoders}, author = {Moor, Michael and Horn, Max and Rieck, Bastian and Borgwardt, Karsten}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {7045--7054}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/moor20a/moor20a.pdf}, url = {https://proceedings.mlr.press/v119/moor20a.html}, abstract = {We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.} }
Endnote
%0 Conference Paper %T Topological Autoencoders %A Michael Moor %A Max Horn %A Bastian Rieck %A Karsten Borgwardt %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-moor20a %I PMLR %P 7045--7054 %U https://proceedings.mlr.press/v119/moor20a.html %V 119 %X We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.
APA
Moor, M., Horn, M., Rieck, B. & Borgwardt, K.. (2020). Topological Autoencoders. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:7045-7054 Available from https://proceedings.mlr.press/v119/moor20a.html.

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